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A Property Tester for Tree-Likeness of Quartet Topologies

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Abstract

Property testing is a rapid growing field in theoretical computer science. It considers the following task: given a function f over a domain D, a property ℘ and a parameter 0<ε<1, by examining function values of f over o(|D|) elements in D, determine whether f satisfies ℘ or differs from any one which satisfies ℘ in at least ε|D| elements. An algorithm that fulfills this task is called a property tester. We focus on tree-likeness of quartet topologies, which is a combinatorial property originating from evolutionary tree construction. The input function is f Q , which assigns one of the three possible topologies for every quartet over an n-taxon set S. We say that f Q satisfies tree-likeness if there exists an evolutionary tree T whose induced quartet topologies coincide with f Q . In this paper, we prove the existence of a set of quartet topologies of error number at least \(c{n\choose 4}\) for some constant c>0, and present the first property tester for tree-likeness of quartet topologies. Our property tester makes at most O(n 3/ε) queries, and is of one-sided error and non-adaptive.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi, 621, Taiwan

    Maw-Shang Chang & Chuang-Chieh Lin

  2. Department of Computer Science, RWTH Aachen University, Ahornstr. 55, 52056, Aachen, Germany

    Peter Rossmanith

Authors
  1. Maw-Shang Chang
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  2. Chuang-Chieh Lin
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  3. Peter Rossmanith
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Correspondence to Chuang-Chieh Lin.

Additional information

This research was supported by the National Science Council of Taiwan under grant no. NSC 96-2221-E-194-045-MY3, and partially supported by NSC-DAAD Sandwich Program.

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Chang, MS., Lin, CC. & Rossmanith, P. A Property Tester for Tree-Likeness of Quartet Topologies. Theory Comput Syst 49, 576–587 (2011). https://doi.org/10.1007/s00224-010-9276-5

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